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Two-Stage Huber Estimation

Author

Listed:
  • Christophe Muller

    (Universidad de Alicante)

  • Tae-Hwan Kim

    (Yonsei University)

Abstract

In this paper we study how the Huber estimator can be adapted to the presence of endogeneity in a two stage equations setting similar to that of 2SLS. We propose an estimation procedure that is at the same time relatively (i) simple, (ii) robust and (iii) efficient. Moreover, we deal with the case of random regressors and asymmetric errors, two extensions rarely present in this literature. The preliminary scale correction is implemented with median absolute deviation estimator, which is consistent with our above criteria and is a very robust estimator of scale. The resulting estimator is termed as the Two-Stage Huber (2SH) estimator. We explicitly establish the conditions for consistency and asymptotic normality of the 2SH estimator and we derive the formula of the asymptotic covariance matrix. We conduct Monte Carlo simulations whose results indicate that the 2SH estimator has smaller standard errors than the Two-Stage Least Squares (2SLS) estimator and than the Two-Stage Least Absolute Deviations (2SLAD) estimator in many situations. On the whole, the 2SH estimator appears to be a simple and useful alternative to 2SLS and 2SLAD in cases of two-stage estimation to deal with endogeneity when there are concerns for both robustness and efficiency.

Suggested Citation

  • Christophe Muller & Tae-Hwan Kim, 2005. "Two-Stage Huber Estimation," Working Papers. Serie AD 2005-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2005-17
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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2005-17.pdf
    File Function: Fisrt version / Primera version, 2005
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    References listed on IDEAS

    as
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    Cited by:

    1. Pavel Cizek & Wolfgang Härdle, 2006. "Robust Econometrics," SFB 649 Discussion Papers SFB649DP2006-050, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Zhelonkin, Mikhail & Genton, Marc G. & Ronchetti, Elvezio, 2012. "On the robustness of two-stage estimators," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 726-732.

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    Keywords

    Two-stage estimation; Huber estimation; robustness; endogeneity;
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